The Three Hundred Project: The relationship between the shock and splashback radii of simulated galaxy clusters
Observations of the intracluster medium (ICM) in the outskirts of galaxy clusters reveal shocks associated with gas accretion from the cosmic web. Previous work based on non-radiative cosmological hydrodynamical simulations have defined the shock radius, $r_\text{shock}$, using the ICM entropy, $K \propto T/{n_\mathrm{e}}^{2/3}$, where $T$ and $n_\text{e}$ are the ICM temperature and electron density respectively; the $r_\text{shock}$ is identified with either the radius at which $K$ is a maximum or at which its logarithmic slope is a minimum. We investigate the relationship between $r_\text{shock}$, which is driven by gravitational hydrodynamics and shocks, and the splashback radius, $r_\text{splash}$, which is driven by the gravitational dynamics of cluster stars and dark matter and is measured from their mass profile. Using 324 clusters from {\small The Three Hundred} project of cosmological galaxy formation simulations, we quantify statistically how $r_\text{shock}$ relates to $r_\text{splash}$. Depending on our definition, we find that the median $r_\text{shock} \simeq 1.38 r_\text{splash} (2.58 R_{200})$ when $K$ reaches its maximum and $r_\text{shock} \simeq 1.91 r_\text{splash} (3.54 R_{200})$ when its logarithmic slope is a minimum; the best-fit linear relation increases as $r_\text{shock} \propto 0.65 r_\text{splash}$. We find that $r_\text{shock}/R_{200}$ and $r_\text{splash}/R_{200}$ anti-correlate with virial mass, $M_{200}$, and recent mass accretion history, and $r_\text{shock}/r_\text{splash}$ tends to be larger for clusters with higher recent accretion rates. We discuss prospects for measuring $r_\text{shock}$ observationally and how the relationship between $r_\text{shock}$ and $r_\text{splash}$ can be used to improve constraints from radio, X-ray, and thermal Sunyaev-Zeldovich surveys that target the interface between the cosmic web and clusters.